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Graphene has demonstrated great potential in new-generation electronic applications due to its unique electronic properties such as large carrier Fermi-velocity, ultrahigh carrier mobility and high material stability. Interestingly, in multilayer graphene, the electronic structures can be further engineered by the introduction of a twist angle between different layers to create van Hove singularities (vHSs). With largely enhanced carrier density of states, vHSs can lead to enhanced optical absorption for selective photon energies. Since the binding energy of vHSs can be tuned by twist angle, twisted bi- and multilayer graphene provides a promising material base for fabricating wavelength-selective ultrafast photodetectors.
However, despite the consensus on the existence of vHSs for small twist angles (≤5°), the possibility of vHS formation in large twist angles is still under debate. To settle this discrepancy, systematic investigation on the electronic structure of twisted bi- and multilayer graphene over a wide twist angle regime is urged. Although the electronic structures of crystalline materials can be readily studied by the angle resolved photoemission spectroscopy (ARPES), the limited spatial resolution (typically hundreds of micrometres) makes it unsuitable for this task, as the grain size of twisted multilayer graphene is typically up to tens of micrometres. Therefore, the recent development of ARPES with sub-micrometre spatial resolution (i.e. micro-ARPES) provides an excellent opportunity for investigating the electronic structures of such multi-layer graphene domains with varying twist angles.
In the present work, we carry out micro-ARPES studies at the Spectromicroscopy beamline of Elettra. The principle of the measurement is briefed in Figure 1a, wherethe X-ray beam from the beamline is focused onto the sample down to a spot of ~0.8 μm in size. Multilayer graphene samples with different twist angles grown on copper substrate are scanned to give the 2D photoemission spectral intensity map, which not only shows the location of the graphene domains, but also shows clear difference in the contrast map for graphene of different thickness ranging from 1-5 layers.

Figure 1. a) Illustration of micro-ARPES operational principle. A Schwarzschild mirror (as shown here) or a Fresnel zone plate achieves micro focusing of the synchrotron light. b) Large-scale spatial scanning image of the sample in the spectral range of the copper d-bands. Dots with different color mark selected positions for subsequent measurement. c) Energy-momentum-dispersions taken at positions shown in b). Red dashed lines indicate the energy of the Dirac point (ED) in each spectrum of the top layer. Red solid curves are integrated EDCs for each spectrum, which are corrected by the Fermi-Dirac distribution, allowing to see features near the Fermi Surface. d) Evolution of ED of the top layer with total number of layers. The blue line indicates a fit of the data using the capacitor-model which is discussed in detail in the reference.

Due to the chemical potential difference between the Cu substrate and graphene layers, electrons are transferred from the copper substrate to graphene to fill its unoccupied states, thus causing the substrate doping effect, which naturally decrease with the thickness of the graphene domains. Indeed, such substrate doping effect are directly observed by our measurement, as shown in Figure 1d, the dependence of the upshift of the Fermi level (with respect to the Dirac point position) with the graphene layer thickness clearly show the substrate doping effect and can be well accounted by our theoretical model.Besides the substrate doping effect, we investigate the vHSs across multi-layer graphene domains over a broad range of twist angle. As examples, Figures 2a, b demonstrate the morphology and the related band dispersions of twisted bilayer graphene (tBLG, measured from P1 in Figure 2a) and trilayer graphene (tTLG, measured from P2 in Figure 2a), respectively, with the band structures of tBLG (Figure 2b, P1) and tTLG showing one and two vHSs, respectively. The systematic study of the evolution of vHS energy with twist angle ranging from 5° to 31° are then carried out, and the results are summarised in Figure 2c. The evolution of the vHS binding energy can again be well reproduced by our theoretical model. as illustrated in Figure 2a.

Figure 2. a) Upper panel: spatial scanning image of the region of interest. The red dashed line marks the misalignment between the first and the second layer of graphene lattice. Lower panel: illustration of the band structure near K points of tBLG with twisted angle θ. b) Electronic band structure measured on the points marked by the red cross in a). P1 is for twisted bilayer graphene (tBLG) and P2 is for twisted trilayer graphene (tTLG). c) Relationship between twist angle and EvHS; the red and blue dots indicate the experimental results, while the black line is the predicted evolution by the theoretical model (for more details, see the reference), showing the nonlinearity of the vHS binding energy at large twist angles. d) Photodetector showing large photocurrent under the illumination of corresponding wavelength due to the vHS binding energy. Upper panel: optical image of the device with two regions of tBLG with varying twist angle. The device is under the illumination of a 532 nm laser and photocurrent is measured. The insets show that the vHS pair will result in large response to the impeding laser with the photon energy that double the vHS binding energy. Lower panel: real space mapping of the photocurrent during illumination. The two twist angle regions respond differently to the excitation wavelength.

Given the greatly enhanced carrier density of states at the vHS binding energy, twisted multilayer graphene can be used in high efficiency photodetectors that is sensitive to specific photon energies (Ephoton=2EνHS). Furthermore, the broad tunablity of the vHS binding energy (by changing the twist angle) demonstrated from the measurements (up to 2.5 eV, see Figure 2c) guarantees the broad operation range from infrared to ultraviolet (up to 5 eV) photons. To demonstrate such application potential, a proof-of-concept device has been fabricated (Figure 2d). Remarkably, in the region where the resonance absorption condition is met (Ephoton=2EνHS), the photocurrent is dramatically enhanced (by 600%) compared to unmatched region, clearly demonstrating the feasibility and potential of the wavelength-selection application.